Magnetic Properties of Solids
Magnetic Properties of Solids Solids can be divided into different classes depending on their response to magnetic fields. (a) Paramagnetic (Weakly magnetic): Such materials contain permanent magnetic dipoles due to the presence of atoms, ions or molecules with unpaired electrons e.g. and They are attracted by the magnetic field. They, however, lose their magnetism in the absence of a magnetic field. (b) Diamagnetic: They are weakly repelled by magnetic fields. Diamagnetism arises due to the absence of unpaired electrons e.g. (18...
read moreStoichiometric Defects
Defects in Stoichiometric Solids It is generally known that all the compounds follow law of definite proportion. But there are certain solid compounds which, refuse to obey this universal law. Such solid compounds which actually do not possess the exact compositions according to the electronic considerations have been given the name Berthollide or non-stoichiometric compounds. For example, in certain oxides such as Metallic hydrides as , ,sulphides as ; tungsten bronzes as , etc., there is between the atoms and hence they are termed...
read moreCrystal Defects
Crystal Defects An ideal crystal is one which has the same unit cell containing the same lattice points throughout the whole of the crystal. However, a number of crystals reflect the absence of perfectness in the arrangement of the lattice points. These defects were studied by Frenkel (1930). These are of the following types: 1. Point Defects: These defects arise due to a few lattice points. They are of two types: (a) Valency defects: If an atom or ion is missing from the lattice site, the defect in the -crystal is called valency...
read moreBragg’s Equation
Bragg’s Equation This equation gives a simple relationship between the wavelength of X-rays and the distance between the planes in the crystal and the angle of reflection. The equation may be written as: where n = order of reflection; in general it is taken as = wavelength of X-rays, d = distance between two layers of the crystals and =angle of incident light. Example 1: Inter planar distance between two layers is in a crystal. Calculate the angle of reflection for first order reflection. X-rays of wavelength are diffracted by...
read moreLimiting Radius Ratios
Limiting radius ratios An ionic crystal contains a large number of cations and, anions. Generally, cations are smaller in size than anions. The cations are surrounded by anions and they touch each other. These ions are arranged in space in such a way as to produce maximum stability. The stability of the ionic crystals may be described in terms of radius ratio, I.e, the ratio of the radius of cation (r) to that of anion (R) (r / R). The range of (r/ R) may be expressed as limiting radius ratio. This value is important to determine the...
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Interstices in Crystals It has been shown that the particles are closely packed in the crystals even then there is some empty space left in between the spheres. This is known as interstices (or interstitial site of holes or empty space or voids). The interstices are of two types: (i) Tetrahedral-interstices: We have seen that in hexagonal close packing (hcp) and cubic close packing (ccp) each sphere of second layer touches three spheres of first layer. Thus they, leave a small space in between which is known as tetrahedral site or interstices....
read moreDensity of Crystal
Theoretical density of the crystal If the length of edge of the unit cell is known we can calculate the density of the crystal as follows: Let length of edge of the unit cell be l. Volume of the unit cell = Density of the unit cell = Mass number of the unit cell = number of atoms in a unit cell × Mass of one atom = n × mg But mass of one atom(m) = Mass of the unit cell Number of atoms in a unit cell Mass of one atom Example 1. An element (atomic mass = 60) having face-centred cubic crystal has a density of . What is the...
read moreCubic Unit Cell
Cubic unit cell There are three types of cubic unit cells which are (i) Simple cubic (ii) Body centered cubic (iii) Face centered cubic. These unit cells are formed by different number of atoms or ions, which are as follows: (i) Simple cubic unit cell: In this case one atom or ion lies at each corner of the cube. Since only 1/8 of each corner sphere lies within the unit cell hence simple cubic unit cell contains a total (1/8) 8 =1, atom or ion. The volume occupied by the particles in simple cubic unit cell is 52.4% and open space in this...
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Close packing of identical solid spheres The solids which have non-directional bonding, their structures are determined on the basis of geometrical consideration. For such solids, it is found that the lowest energy structure is that in which each particle is surrounded by the greatest possible number of neighbours. In order to understand the structures of such solids, let us consider the particles as hard sphere of equal size in three directions. Although there are many ways to arrange the hard spheres but the one in which maximum available...
read moreSpacing of Planes
Spacing of Planes The distance between successive lattice planes of the same type is called the spacing of planes or inter-planar distance between the planes. On the basis of this aspect, the lattices may be divided into following classes: 1. Simple cubic lattice: “When one only unit is situated at each corner of the cubic cell, it is known as simple cubic lattice”. In other words, it contains eight points situated at eight corners of a cube. There is no lattice point inside the cube. 2. The body centered cubic (bcc) lattice; “When one...
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